Some weak separation axioms

Open sets are the building block of topological spaces. Separation axioms, connectedness, compactness, continuous function etc. many concepts such as open and closed sets are defined. Moreover, the results of the modifications to the open set concept have been the subject studied for years. N. Levine defined a semi-open (semi-closed) set in a topological space as a set A such that there exists an open U⊆X such that U⊆A⊆U ̅. On the other hand, the concept of pre-open (pre-closed) and precontiunity in topological spaces was first introduced by A. S. Mashhour. Mashhour has defined that subset A in a topological space is A⊆(A ̅ )^∘ to be pre-open. After Levine and Mashhour's works on semi-closed and pre-closed sets, many mathematicians have turned their attention into generalizations of various concepts in topology, considering the notions of semi-closed and pre-closed sets. They generalized the concept of closed sets to semi-generalized (pre-generalized) closed sets with the help of semi-closedness (pre-closedness). In this thesis, the characteristics of some weak separation axioms based on the notions of semi-open (pre-open) closed, sg(pg)-closed closed, their relations and equivalences are shown.